DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction

2025-04-28

AI Summary

This work addresses the challenge of forecasting states for unknown time-varying partial differential equation (PDE) systems characterized exclusively by short trajectory data. Method: We propose a decoupled state prediction framework: first explicitly discovering the governing evolution operator from short sequences, then performing next-state prediction via numerical time integration. Our core innovation is the “operator discovery” paradigm—decoupling dynamical modeling from state evolution—and introducing a hypernetwork to generate lightweight operator-network parameters, enabling cross-physics generalization and efficient pretraining. The methodology comprises multi-physics joint pretraining followed by downstream fine-tuning. Results: Experiments demonstrate state-of-the-art (SOTA) performance across multiple PDE forecasting benchmarks with significantly reduced training epochs. The pre-trained model exhibits strong generalization across diverse physical domains, and fine-tuned variants consistently maintain top-tier accuracy.

Technology Category

• Search and Optimization: Learning to Search
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We address the problem of predicting the next state of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to this task, the presence of a well-structured evolution operator in the data suggests a more tailored and efficient approach. Specifically, when the PDE is fully known, classical numerical solvers can evolve the state accurately with only a few parameters. Building on this observation, we introduce DISCO, a model that uses a large hypernetwork to process a short trajectory and generate the parameters of a much smaller operator network, which then predicts the next state through time integration. Our framework decouples dynamics estimation (i.e., DISCovering an evolution operator from a short trajectory) from state prediction (i.e., evolving this operator). Experiments show that pretraining our model on diverse physics datasets achieves state-of-the-art performance while requiring significantly fewer epochs. Moreover, it generalizes well and remains competitive when fine-tuned on downstream tasks.

Problem

• Predict next state of unknown PDE-governed dynamical systems
• Discover efficient evolution operator from short trajectory
• Generalize across diverse physics with few epochs

Innovation

• Hypernetwork generates small operator network parameters
• Decouples dynamics estimation from state prediction
• Pretrains on diverse datasets for generalization